Valuations of lines
Mlček, Josef
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 667-679 / Harvested from Czech Digital Mathematics Library
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We enlarge the problem of valuations of triads on so called lines. A line in an $e$-structure $\Bbb A = \langle A,F,E\rangle$ (it means that $\langle A,F\rangle$ is a semigroup and $E$ is an automorphism or an antiautomorphism on $\langle A,F\rangle$ such that $E\circ E = {\text{$\bold {Id}$}}\restriction A$) is, generally, a sequence $\Bbb A\restriction B$, $\Bbb A \restriction U _c$, $c\in {\text{$\bold {FZ}$}}$ (where ${\text{$\bold {FZ}$}}$ is the class of finite integers) of substructures of $\Bbb A$ such that $B\subseteq U_c \subseteq U_d$ holds for each $c\leq d$. We denote this line as $\Bbb A (U_c ,B)_{c\in {\text{$\bold {FZ}$}}}$ and we say that a mapping $H$ is a valuation of the line $\Bbb A (U_c ,B)_{c\in {\text{$\bold {FZ}$}}}$ in a line $\hat{\Bbb A} (\hat{U}_c ,\hat{B})_{c\in {\text{$\bold {FZ}$}}}$ if it is, for each $c\in {\text{$\bold {FZ}$}}$, a valuation of the triad $\Bbb A (U_c,B)$ in $\hat{\Bbb A} (\hat{U}_c,\hat{B})$. Some theorems on an existence of a valuation of a given line in another one are presented and some examples concerning equivalences and ideals are discussed. A generalization of the metrization theorem is presented, too.

Publié le : 1992-01-01
Classification:  03E70,  20M14,  20M99,  54E35 
@article{118538,
     author = {Josef Ml\v cek},
     title = {Valuations of lines},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {667-679},
     zbl = {0784.03033},
     mrnumber = {1240188},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118538}
}

Mlček, Josef. Valuations of lines. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 667-679. http://gdmltest.u-ga.fr/item/118538/

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